Finite Group Databasebeta

← C3×#65250 #11749858

Subgroups — C3×#65250 #11749858

Order 960.

476 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊D5C211yesmaximal, characteristic
2C2×C3×C5×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×C22⋊Dic5C211yesmaximal, characteristic, complemented
4C2×C3×#685C211yesmaximal, characteristic, complemented
5C2×C3×#685C211yesmaximal, characteristic, complemented
6C2×C3×C4⋊Dic5C211yesmaximal, characteristic, complemented
7C3×#3963C211yesmaximal, characteristic, complemented
8#65250C311yesmaximal, characteristic, direct product factor, Hall
9C24×C3×C5C2211yescharacteristic
10C23×C3×D5C2211yescharacteristic
11C22×C3×C4×C5C2211yescharacteristic
12C22×C3×C4×C5C2211yescharacteristic
13C2×C3×C22⋊D5—22no—
14C2×C3×C22⋊D5—22no—
15C2×C3×C22⋊D5—22no—
16C22×C3×Dic5C2211yescharacteristic
17C22×C3×Dic5C2211yescharacteristic
18C22×C3×Dic5C2211yescharacteristic
19C3×C5×C22⋊C4—22no—
20C3×C22⋊Dic5—22no—
21C3×#685—22no—
22C3×#685—22no—
23C3×C4⋊Dic5—22no—
24C3×#394—51nomaximal, Hall
25C22×C22⋊D5C2×C311yescharacteristic
26C2×C5×C22⋊C4C2×C311yescharacteristic, complemented
27C2×C22⋊Dic5C2×C311yescharacteristic, complemented
28C2×#685C2×C311yescharacteristic, complemented
29C2×#685C2×C311yescharacteristic, complemented
30C2×C4⋊Dic5C2×C311yescharacteristic, complemented
31#3963C2×C311yescharacteristic, complemented
32C23×C3×C5—21no—
33C23×C3×C5—21no—
34C23×C3×C5—21no—
35C23×C3×C5—21no—
36C23×C3×C5—21no—
37C23×C3×C5—21no—
38C23×C3×C5D412yes—
39C23×C3×C5C2311yescharacteristic
40C22×C3×D5—21no—
41C22×C3×D5—21no—
42C22×C3×D5—21no—
43C22×C3×D5—21no—
44C22×C3×D5—21no—
45C22×C3×D5—21no—
46C22×C3×D5D412yes—
47C2×C3×C4×C5—21no—
48C2×C3×C4×C5—21no—
49C2×C3×C4×C5—21no—
50C2×C3×C4×C5—21no—
51C2×C3×C4×C5—21no—
52C2×C3×C4×C5D412yescomplemented
53C3×C22⋊D5—28no—
54C2×C3×Dic5—21no—
55C2×C3×Dic5—21no—
56C2×C3×Dic5—21no—
57C2×C3×Dic5—21no—
58C2×C3×Dic5—21no—
59C2×C3×Dic5—21no—
60C2×C3×Dic5—21no—
61C2×C3×Dic5—21no—
62C2×C3×Dic5D412yes—
63C22×C3×D4—51no—
64C2×C3×C4⋊C4—51no—
65C2×C3×C22⋊C4—51no—
66C2×C3×C22⋊C4—51no—
67C2×C3×C22⋊C4—51no—
68C2×C3×C22⋊C4D511yescharacteristic, complemented
69C3×#95—51no—
70C24×C5C22×C311yescharacteristic
71C23×D5C22×C311yescharacteristic
72C22×C4×C5C22×C311yescharacteristic
73C22×C4×C5C22×C311yescharacteristic
74C2×C22⋊D5—22no—
75C2×C22⋊D5—22no—
76C2×C22⋊D5—22no—
77C22×Dic5C22×C311yescharacteristic
78C22×Dic5C22×C311yescharacteristic
79C22×Dic5C22×C311yescharacteristic
80C5×C22⋊C4—22no—
81C22⋊Dic5—22no—
82#685—22no—
83#685—22no—
84C4⋊Dic5—22no—
85#394—51noSylow
86C22×C3×C5—22no—
87C22×C3×C5—22no—
88C22×C3×C5—22no—
89C22×C3×C5—41no—
90C22×C3×C5—41no—
91C22×C3×C5—41no—
92C22×C3×C5—41no—
93C22×C3×C5C2×D411yescharacteristic
94C22×C3×C5C2×D411yescharacteristic
95C22×C3×C5C2×D411yescharacteristic
96C22×C3×C5C2×D411yescharacteristic
97C22×C3×C5#4111yescharacteristic
98C22×C3×C5#4111yescharacteristic
99C22×C3×C5#4111yescharacteristic
100C2×C3×D5—22no—
101C2×C3×D5—22no—
102C2×C3×D5—22no—
103C2×C3×D5—41no—
104C2×C3×D5—41no—
105C2×C3×D5—41no—
106C2×C3×D5—41no—
107C3×C4×C5—22no—
108C3×C4×C5—41no—
109C3×Dic5—22no—
110C3×Dic5—41no—
111C3×Dic5—41no—
112C24×C3—51no—
113C24×C3C2×D511yescharacteristic
114C2×C3×D4—102no—
115C2×C3×D4—102no—
116C2×C3×D4—102no—
117C22×C3×C4—51no—
118C22×C3×C4—51no—
119C22×C3×C4—51no—
120C22×C3×C4C2×D511yescharacteristic
121C22×C3×C4C2×D511yescharacteristic
122C3×C4⋊C4—102no—
123C3×C22⋊C4—22no—
124C3×C22⋊C4—102no—
125C3×C22⋊C4—102no—
126C3×C22⋊C4—102no—
127C23×C5—21no—
128C23×C5—21no—
129C23×C5—21no—
130C23×C5—21no—
131C23×C5—21no—
132C23×C5—21no—
133C23×C5C3×D412yes—
134C23×C5C23×C311yescharacteristic
135C22×D5—21no—
136C22×D5—21no—
137C22×D5—21no—
138C22×D5—21no—
139C22×D5—21no—
140C22×D5—21no—
141C22×D5C3×D412yes—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5C3×D412yescomplemented
148C22⋊D5—28no—
149C2×Dic5—21no—
150C2×Dic5—21no—
151C2×Dic5—21no—
152C2×Dic5—21no—
153C2×Dic5—21no—
154C2×Dic5—21no—
155C2×Dic5—21no—
156C2×Dic5—21no—
157C2×Dic5C3×D412yes—
158C22×D4—51no—
159C2×C4⋊C4—51no—
160C2×C22⋊C4—51no—
161C2×C22⋊C4—51no—
162C2×C22⋊C4—51no—
163C2×C22⋊C4C3×D511yescharacteristic, complemented
164#95—51no—
165C2×C3×C5—42no—
166C2×C3×C5#12011yescharacteristic
167C2×C3×C5#12111yescharacteristic
168C2×C3×C5#12111yescharacteristic
169C2×C3×C5#12111yescharacteristic
170C2×C3×C5#12311yescharacteristic
171C2×C3×C5#12311yescharacteristic
172C2×C3×C5#12411yescharacteristic
173C3×D5—42no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3—21no—
177C23×C3—21no—
178C23×C3—21no—
179C23×C3—21no—
180C23×C3—52no—
181C23×C3—101no—
182C23×C3—101no—
183C23×C3—101no—
184C23×C3—101no—
185C23×C3—101no—
186C23×C3—101no—
187C23×C3D2012yes—
188C23×C3C22×D511yescharacteristic
189C3×D4—108no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—52no—
196C2×C3×C4—101no—
197C2×C3×C4—101no—
198C2×C3×C4—101no—
199C2×C3×C4—101no—
200C2×C3×C4—101no—
201C2×C3×C4—101no—
202C2×C3×C4—101no—
203C2×C3×C4—101no—
204C2×C3×C4C22⋊D512yescomplemented
205C22×C5—22no—
206C22×C5—22no—
207C22×C5—22no—
208C22×C5—41no—
209C22×C5—41no—
210C22×C5—41no—
211C22×C5—41no—
212C22×C5C2×C3×D411yescharacteristic
213C22×C5C2×C3×D411yescharacteristic
214C22×C5C2×C3×D411yescharacteristic
215C22×C5C2×C3×D411yescharacteristic
216C22×C5C3×#4111yescharacteristic
217C22×C5C3×#4111yescharacteristic
218C22×C5C3×#4111yescharacteristic
219C2×D5—22no—
220C2×D5—22no—
221C2×D5—22no—
222C2×D5—41no—
223C2×D5—41no—
224C2×D5—41no—
225C2×D5—41no—
226C4×C5—22no—
227C4×C5—41no—
228Dic5—22no—
229Dic5—41no—
230Dic5—41no—
231C24—51no—
232C24C2×C3×D511yescharacteristic
233C2×D4—102no—
234C2×D4—102no—
235C2×D4—102no—
236C22×C4—51no—
237C22×C4—51no—
238C22×C4—51no—
239C22×C4C2×C3×D511yescharacteristic
240C22×C4C2×C3×D511yescharacteristic
241C4⋊C4—102no—
242C22⋊C4—22no—
243C22⋊C4—102no—
244C22⋊C4—102no—
245C22⋊C4—102no—
246C3×C5#39411yescharacteristic, complemented, Hall
247C22×C3—22no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3—41no—
251C22×C3—41no—
252C22×C3—41no—
253C22×C3—41no—
254C22×C3—102no—
255C22×C3—102no—
256C22×C3—102no—
257C22×C3—201no—
258C22×C3—201no—
259C22×C3—201no—
260C22×C3—201no—
261C22×C3C2×D2011yescharacteristic
262C22×C3#70911yescharacteristic
263C22×C3D4×D511yescharacteristic
264C22×C3D4×D511yescharacteristic
265C22×C3#71111yescharacteristic
266C22×C3#71111yescharacteristic
267C22×C3C2×C22⋊D511yescharacteristic
268C3×C4—22no—
269C3×C4—41no—
270C3×C4—102no—
271C3×C4—201no—
272C3×C4—201no—
273C2×C5—42no—
274C2×C5C3×#12011yescharacteristic
275C2×C5C3×#12111yescharacteristic
276C2×C5C3×#12111yescharacteristic
277C2×C5C3×#12111yescharacteristic
278C2×C5C3×#12311yescharacteristic
279C2×C5C3×#12311yescharacteristic
280C2×C5C3×#12411yescharacteristic
281D5—42no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—52no—
289C23—101no—
290C23—101no—
291C23—101no—
292C23—101no—
293C23—101no—
294C23—101no—
295C23C3×D2012yes—
296C23C22×C3×D511yescharacteristic
297D4—108no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—52no—
304C2×C4—101no—
305C2×C4—101no—
306C2×C4—101no—
307C2×C4—101no—
308C2×C4—101no—
309C2×C4—101no—
310C2×C4—101no—
311C2×C4—101no—
312C2×C4C3×C22⋊D512yescomplemented
313C2×C3—42no—
314C2×C3—202no—
315C2×C3#402811yescharacteristic
316C2×C3#402911yescharacteristic
317C2×C3#403111yescharacteristic
318C2×C3#403211yescharacteristic
319C2×C3#407611yescharacteristic
320C2×C3#408411yescharacteristic
321C2×C3#408511yescharacteristic
322C5C3×#39411yescharacteristic, complemented, Sylow
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—102no—
331C22—102no—
332C22—102no—
333C22—201no—
334C22—201no—
335C22—201no—
336C22—201no—
337C22C2×C3×D2011yescharacteristic
338C22C3×#70911yescharacteristic
339C22C3×D4×D511yescharacteristic
340C22C3×D4×D511yescharacteristic
341C22C3×#71111yescharacteristic
342C22C3×#71111yescharacteristic
343C22C2×C3×C22⋊D511yescharacteristic
344C4—22no—
345C4—41no—
346C4—102no—
347C4—201no—
348C4—201no—
349C3#6525011yescharacteristic, direct product factor, Sylow
350C2—42no—
351C2—202no—
352C2C3×#402811yescharacteristic
353C2C3×#402911yescharacteristic
354C2C3×#403111yescharacteristic
355C2C3×#403211yescharacteristic
356C2C3×#407611yescharacteristic
357C2C3×#408411yescharacteristic
358C2C3×#408511yescharacteristic
subgroupG/H
centerC23×C3C22×D5
commutator, cosocleC23×C5C23×C3
FrattiniC23C22×C3×D5
FittingC2×C3×C5×C22⋊C4C2
socleC23×C3×C5C23
prime radicalC22×C3×C22⋊D5C2
hypercenterC2×C3×C22⋊C4D5
hypocenterC5C3×#394
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C3×C5×C22⋊C4C2semidirect
3. C2×C3×C22⋊Dic5C2semidirect
4. C2×C3×#685C2semidirect
5. C2×C3×#685C2semidirect
6. C2×C3×C4⋊Dic5C2semidirect
7. C3×#3963C2semidirect
8. #65250C3direct (N × H)
26. C2×C5×C22⋊C4C2×C3semidirect
27. C2×C22⋊Dic5C2×C3semidirect
28. C2×#685C2×C3semidirect
29. C2×#685C2×C3semidirect
30. C2×C4⋊Dic5C2×C3semidirect
31. #3963C2×C3semidirect
52. C2×C3×C4×C5D4semidirect
68. C2×C3×C22⋊C4D5semidirect
147. C2×C4×C5C3×D4semidirect
163. C2×C22⋊C4C3×D5semidirect
204. C2×C3×C4C22⋊D5semidirect
246. C3×C5#394semidirect
312. C2×C4C3×C22⋊D5semidirect
322. C5C3×#394semidirect
349. C3#65250direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×C22⋊D52
C2×C3×C5×C22⋊C42
C2×C3×C22⋊Dic52
C2×C3×#6852
C2×C3×C4⋊Dic52
C3×#39632
#652503
C3×#3945